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 A157458 Triangle, read by rows, double tent function: T(n,k) = min(1 + 2*k, 1 + 2*(n-k), n). 2
 0, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 3, 4, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 6, 5, 3, 1, 1, 3, 5, 7, 7, 5, 3, 1, 1, 3, 5, 7, 8, 7, 5, 3, 1, 1, 3, 5, 7, 9, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 10, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 11, 11, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 11, 12, 11, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 11, 13, 13, 11, 9, 7, 5, 3, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The general form of this, and related triangular sequences, takes the form A(n, k, m) = (m*(n-k) + 1)*A(n-1, k-1, m) + (m*k + 1)*A(n-1, k, m) + m*f(n, k)* A(n-2, k-1, m), where f(n,k) is a polynomial in n and k. Row sums are: 0, 2, 4, 8, 12, 18, 24, 32, 40, 50, 60, ... = A007590(n+1). - N. J. A. Sloane, Aug 27 2009 LINKS Nathaniel Johnston, Table of n, a(n) for n = 0..10000 FORMULA T(n, k) = min(1 + 2*k, 1 + 2*(n - k), n). From Yu-Sheng Chang, May 19 2020: (Start) O.g.f.: F(z,v) = (1+v)*z/((1-v*z-1)*(1-z)*(1-v*z^2)). T(n,k) = [v^k] (1+v)*(2*v^(n+1)+2-((sqrt(v)-1)^2 * (-1)^n + (sqrt(v)+1)^2) * v^((1/2)*n))/(2*(v-1)^2). (End) EXAMPLE Triangle begins as:   0;   1, 1;   1, 2, 1;   1, 3, 3, 1;   1, 3, 4, 3, 1;   1, 3, 5, 5, 3, 1;   1, 3, 5, 6, 5, 3, 1;   1, 3, 5, 7, 7, 5, 3, 1;   1, 3, 5, 7, 8, 7, 5, 3, 1;   1, 3, 5, 7, 9, 9, 7, 5, 3, 1;   1, 3, 5, 7, 9, 10, 9, 7, 5, 3, 1; MAPLE T := proc(m, n) return min(1+2*m, 1+2*(n-m), n): end: seq(seq(T(m, n), m=0..n), n=0..14); # Nathaniel Johnston, Apr 29 2011 MATHEMATICA T[n_, k_]:= Min[1+2*k, 1+2*(n-k), n]; Table[T[n, k], {n, 0, 14}, {k, 0, n}]//Flatten CROSSREFS Cf. A003983, A157457. Sequence in context: A155582 A169946 A160832 * A174447 A174374 A242641 Adjacent sequences:  A157455 A157456 A157457 * A157459 A157460 A157461 KEYWORD nonn,tabl,easy AUTHOR Roger L. Bagula, Mar 01 2009 EXTENSIONS Edited by N. J. A. Sloane, Aug 27 2009 More terms from and partially edited by G. C. Greubel, May 21 2020 STATUS approved

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Last modified December 4 15:36 EST 2021. Contains 349526 sequences. (Running on oeis4.)